# Need help with Physics problem (momentum/collisions)

• Engineering100
In summary, the final velocity of the target after the inelastic collision is 6.98 m/s [W 65° N]. This was determined using the conservation of linear momentum and finding the final velocity in each coordinate. The negative angle represents clockwise rotation and the target is traveling 65 degrees North of West.
Engineering100

## Homework Statement

A 0.800 kg target slides along the ice at 3.0 m/s [W], when it is hit by a 20.0 g arrow moving at 260 m/s [N], as part of a show. Find the final velocity of the target after the inelastic collision.

## Homework Equations

pi= pf
m1 v1i+ m2 v2i = (m1+ m2)vf
pythagorean theorem

## The Attempt at a Solution

v1f= ?

pix= pfx
m1 v1ix+ m2 v_2ix = (m1+ m2)vfx
(0.80)(-3.0)+0=(0.80+0.020) vfx
-2.4=(0.820)vfx
v_fx= -2.93 m/s

piy= pfy
m1 v1iy+ m2 v2iy = (m1+ m2)vfy
0+(0.02)(260)=(0.800+0.02) vfy
vfy=5.2/0.82=6.34 m/s

vf=√(-2.93)^2+(6.34)^2
vf=6.98 m/s

tanθ= -2.93/6.34
θ=25°

Since one of these values are negative, the angle is negative. Relatively speaking what would the angle be. also was this question in general answered correctly?

Yes you used the conservation of linear momentum properly, and successfully applied it to each coordinate individually.

The last step however is wrong, as the ratio should be:

$\tan{\theta}=\frac{6.34}{-2.93}$

Which would give:

$\theta=-65.2^\circ$The negative angle interpretation depends on how you defined your angles. In this case, the angles are defined in the sense such that $\theta=0$ along the "negative x-axis". Therefore a negative angle just represents clockwise rotation as opposed to counter-clockwise rotation. So it is traveling $65^\circ$ in the North-West direction. Make sense?

Normally, for example, $\theta=45^\circ$ would be above the x-axis in the 1st quadrant, whereas $\theta=-45^\circ$ would be below the x-axis in the 4th quadrant. In this case $\theta=45^\circ$ would be in the 3rd quadrant below the x-axis and $\theta=-45^\circ$ would be above the x-axis in the second quadrant.

This is due to the fact that the target is moving initially at an angle $-180^\circ$ which is now taken as $0^\circ$. Does this help?

Last edited:
yes thanks so much, great help

so would that be [W 65° N] or [N 25° W]?

Yes. You did it right, but why did you assume that the target was moving in the negative x direction to start with? There's nothing wrong with this, but I would have had it going in the + x direction (for some reason). Oh well. Potatoes, Potahtoes.

Chet

If I understand what you're saying correctly then it would be $\text{[W } 65^\circ \text{ N]}$ (65 degrees North of West).

Also he did it that way because it specified that it was traveling West, and in introductory physics no one expects people to think like that probably.

electricspit said:
If I understand what you're saying correctly then it would be [W $65^\circ$ N] (65 degrees North of West).

Also he did it that way because it specified that it was traveling West, and in introductory physics no one expects people to think like that probably.

Oh thanks. I didn't notice that [W].

Chet

yes, is [W 65∘ N] the correct angle?

## 1. What is momentum in physics?

Momentum is a fundamental concept in physics that measures an object's mass and velocity. It is defined as the product of an object's mass and its velocity, and is a vector quantity, meaning it has both magnitude and direction.

## 2. How is momentum conserved in collisions?

In a closed system, momentum is always conserved, meaning that the total momentum before a collision is equal to the total momentum after the collision. This can be explained by Newton's Third Law of Motion, which states that for every action, there is an equal and opposite reaction.

## 3. What is an elastic collision?

An elastic collision is a type of collision where no kinetic energy is lost. In other words, the total kinetic energy of the system before the collision is equal to the total kinetic energy after the collision. This type of collision is often seen in idealized situations with no external forces or energy loss.

## 4. How do you calculate the momentum of an object?

The momentum of an object can be calculated by multiplying its mass by its velocity. The formula for momentum is p=mv, where p is momentum, m is mass, and v is velocity. The unit for momentum is kg*m/s.

## 5. Can momentum be negative?

Yes, momentum can be negative. This means that the object is moving in the opposite direction of its defined positive direction. For example, if an object is moving to the left and its positive direction is to the right, it would have a negative momentum.

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